| Title: |
ENIGMA: The Geometry of Reasoning and Alignment in Large-Language Models |
| Authors: |
Seneque, Gareth; Ho, Lap-Hang; Saeedi, Nafise Erfanian; Molendijk, Jeffrey; Kuperman, Ariel; Elson, Tim |
| Publication Year: |
2025 |
| Collection: |
ArXiv.org (Cornell University Library) |
| Subject Terms: |
Machine Learning; Artificial Intelligence; Computation and Language; 68T50; I.2.7 |
| Description: |
We present Entropic Mutual-Information Geometry Large-Language Model Alignment (ENIGMA), a novel approach to Large-Language Model (LLM) training that jointly improves reasoning, alignment and robustness by treating an organisation's policies/principles as directions to move on a model's information manifold. Our single-loop trainer combines Group-Relative Policy Optimisation (GRPO), an on-policy, critic-free RL method with Chain-of-Thought (CoT)-format only rewards; a Self-Supervised Alignment with Mutual Information (SAMI)-style symmetric InfoNCE auxiliary; and an entropic Sinkhorn optimal-transport regulariser on hidden-state distributions to bound geometry drift. We also introduce infoNCE metrics that specialise to a standard MI lower bound under matched negatives to measure how strongly a model's CoT encodes these policies. These metrics include a Sufficiency Index (SI) that enables the selection and creation of principles that maximise downstream performance prior to training. In our experiments using small (1B) LLMs, high-SI principles predict steadier training dynamics and improved benchmark performance over GRPO ablations. Our information-geometry analysis of trained models validates desirable structural change in the manifold. These results support our hypothesis that reasoning, alignment, and robustness are projections of a single information-geometric objective, and that models trained using ENIGMA demonstrate principled reasoning without the use of a reward model, offering a path to trusted capability ; 52 pages, 10 figures, author typo corrected, abstract typo corrected |
| Document Type: |
text |
| Language: |
unknown |
| Relation: |
http://arxiv.org/abs/2510.11278 |
| Availability: |
http://arxiv.org/abs/2510.11278 |
| Accession Number: |
edsbas.96BBCC65 |
| Database: |
BASE |